ON THE NOETHER SYMMETRY AND LIE SYMMETRY OF MECHANICAL SYSTEMS

• 来源期刊: 力学学报（英文版）
• 学科: 物理学
• 年，卷（期）: 2002,（4）
• 页码范围: 414-419
• 页数: 6页
• 分类号: O3
• 语种: 英文

摘要

The Noether symmetry is an invariance of Hamilton action under infinitesimal transformations of time and the coordinates. The Lie symmetry is an invariance of the differential equations of motion under the transformations. In this paper, the relation between these two symmetries is proved definitely and firstly for mechanical systems. The results indicate that all the Noether symmetries are Lie symmetries for Lagrangian systems meanwhile a Noether symmetry is a Lie symmetry for the general holonomic or nonholonomic systems provided that some conditions hold.